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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 12

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Answer: \frac{\sin^{4} x}{4}+c

Hint: You must know about the integration rule of trigonometric function.

Given:  \int \sin ^{3}x\cos xdx

Solution: put\sin x=t differentiate both sides, \left [ \frac{d}{dx}\sin x= \cos x \right ]

          \cos x dx=dt

\therefore I= \int t^{3}dt

  =\frac{t^{4}}4{}+c                                                                            \left [ \int x^{n} dx= \frac{x^{n+1}}{n+1} \right ]

   =\frac{\sin^{4} x}{4}+c

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